Roshambo Rock, Paper, Scissors Reference

Authors

Affiliations

Elias Bouacida

University Paris 8

Renaud Foucart

Lancaster University

using DataFrames
import CSV
using StatsBase
using PrettyTables

include("CommonFunctions.jl")
include("RPS.jl")
include("Constants.jl")

Dict{String, String} with 4 entries:
  "Guessing the Paintings" => "painting"
  "Time"                   => "time"
  "Rock, Paper, Scissors"  => "rps"
  "DC-5 Lottery"           => "lottery"

data = createdata(joinpath("..", "Data", "OriginalData", "Rock_Paper_Scissors_Raw_data.csv"), 5)
roshambo = fillstrat(data, 5);

size(roshambo)

(5, 44422)

proportionmap(roshambo[1, :])

Dict{Int64, Float64} with 3 entries:
  2 => 0.356062
  3 => 0.290779
  1 => 0.353158

RPSbyrounds = DataFrame()
for i = 1:5
    res = DataFrame()
    p = proportionmap(roshambo[i, :])
    for (k, v) = p
        res[!, "$k"] = [v]
    end
    append!(RPSbyrounds, res)
end
rename!(RPSbyrounds, "1" => :Rock, "2" => :Paper, "3" => :Scissors)
RPSbyrounds

5×3 DataFrame

Row	Paper	Scissors	Rock
	Float64	Float64	Float64
1	0.356062	0.290779	0.353158
2	0.334519	0.327135	0.338346
3	0.336635	0.318153	0.345212
4	0.32718	0.323353	0.349466
5	0.342916	0.315227	0.341858

confrpsroshambo = set_pt_conf(        
    title = "RPS strategies played by the Roshambo sample.",    
    row_labels = ["Round $i" for i=1:5],
    row_label_alignment = :l,
    alignment = :c, 
    header=["Paper", "Scissors", "Rock"],
    row_label_column_title = "", 
    formatters = (percent_format(2)),
    )

pretty_table_with_conf(confrpsroshambo, RPSbyrounds)

RPS strategies played by the Roshambo sample.
┌─────────┬────────┬──────────┬────────┐
│         │ Paper  │ Scissors │  Rock  │
├─────────┼────────┼──────────┼────────┤
│ Round 1 │ 35.61% │  29.08%  │ 35.32% │
│ Round 2 │ 33.45% │  32.71%  │ 33.83% │
│ Round 3 │ 33.66% │  31.82%  │ 34.52% │
│ Round 4 │ 32.72% │  32.34%  │ 34.95% │
│ Round 5 │ 34.29% │  31.52%  │ 34.19% │
└─────────┴────────┴──────────┴────────┘

open(joinpath("..", "Data", "Output", "TableRPSRoshambo.tex"), "w") do f
    pretty_table_with_conf(confrpsroshambo, f,  RPSbyrounds, backend = Val(:latex), tf = tf_latex_modern)
end

Computing the Best Strategy

universe = ones(Int, 5, 3^5)
c = 0
for i = 1:3, j = 1:3, k = 1:3,l = 1:3, m = 1:3
    c += 1
    universe[:, c] = [i, j, k, l, m]
end

beststrategy = session(universe, roshambo)
beststrategy[!, :index] = collect(1:3^5);

bestindex = beststrategy[beststrategy[!, :SD] .== maximum(beststrategy[!, :SD]), :index]
println("Best strategy: ", (x -> translate(x, RPS_inv)).(universe[:, bestindex]))
println("its probability of winning is ", round(maximum(beststrategy[!, :SD]), digits = 4))
worstindex = beststrategy[beststrategy[!, :SD] .== minimum(beststrategy[!, :SD]), :index]
println("Worst strategy: ",(x -> translate(x, RPS_inv)).(universe[:, worstindex]))
println("its probability of winning is ", round(minimum(beststrategy[!, :SD]), digits = 4))

Best strategy: ["Paper"; "Paper"; "Paper"; "Paper"; "Paper";;]
its probability of winning is 0.5379
Worst strategy: ["Rock"; "Rock"; "Scissors"; "Scissors"; "Rock";;]
its probability of winning is 0.463